As already pointed out, he was a drug user ("I like the Fed-Ex guy because he's a drug dealer and he don't even know it").

But the delivery is his style. Whether it's natural or not I don't know, but it certainly was an integral part of his comedy, similar to the monotone of Steven Wright (whom Mitch Hedberg is the spiritual successor to, in my opinion).

EDIT: Curiously, Hedberg suffered from terrible stage fright. I find him funny to listen to, but almost uncomfortable to watch because he would often stare at the stage or close his eyes.

He had pretty extreme stage fright, hence the sunglasses and staring downward. By all accounts, just a very shy guy with a knack for clever jokes.

That's not very nice.

He was a self-professed drug addict, but his speech was, as far as I know, an affect.